Define pressure. Give the $SI$ and $CGS$ unit of pressure.

Define thrust and pressure and give their unit and dimensional formula.

The densities of ice and water are $\rho$ and $\sigma$ respectively. What is the change in volume when a mass $M$ of ice melts?

Define density. Write its unit and dimensional formula.

At a depth of $1000 \; m$ in an ocean:
$(a)$ What is the absolute pressure?
$(b)$ What is the gauge pressure?
$(c)$ Find the force acting on the window of area $20 \; cm \times 20 \; cm$ of a submarine at this depth,the interior of which is maintained at sea-level atmospheric pressure. (The density of sea water is $1.03 \times 10^3 \; kg \; m^{-3}$,$g = 10 \; m \; s^{-2}$.)

Find the depth of a lake at which the density of water is $1\%$ greater than at the surface. Given the compressibility of water $K = 50 \times 10^{-6} \text{ atm}^{-1}$. (Take $1 \text{ atm} = 10^5 \text{ Pa}$) (in $\text{ km}$)